The present invention relates to methods and apparatus particularly useful for performing a blind deconvolution operation, e.g. for controlling an adjustable linear filter (sometimes called an equalizer) receiving the output of an unknown system in order to produce a desired response for recovering (deconvolving) the input to the system.
The problem of blind deconvolution, as illustrated in FIG. 1 of the drawings, arises when there is an unknown system having an output which is observed, but whose input is unobserved. In such a system it is desired to recover (deconvolve) the input by identifying the inverse of the unknown system. This is done by using an adjustable linear filter (sometimes called an equalizer) which is adjusted to recover, or deconvolve, the input up to a constant shift (delay), and possibly a constant phase or a sign ambiguity.
The problem of blind deconvolution is of considerable interest in many fields of engineering and applied science. For example, in data communication, the unobserved input is a transmitted sequence of data symbols (bits), and the unknown system represents the distortion in the transmission channel (e.g., a telephone line) which causes the undesirable phenomena of inter symbol interference (ISI). The equalizer (adjustable linear filter) in this case attempts to recover the transmitted sequence (i.e., the message) by canceling, or inverting, the distortion caused by the channel.
A similar problem occurs in image restoration or reconstruction, wherein the unobserved input is the original image (scene), and the unknown system represents the imperfections in the electronic or photographic medium which essentially causes blurring effects. The equalizer (adjustable linear filter) in this case attempts to reconstruct the original image by de-blurring, that is canceling the imperfections in the image formation system. This problem is particularly important in fields such as astronomy, remote sensing, and medical imaging, where the blurs cause a severe degradation in the quality and resolution of the observed image. Similar deconvolution problems can be found in the analysis of geophysical signals, in underwater acoustics, and the like.